We wanted to find out using an API how long the phone (web RTC) was connected to the edge. There is an option to "Select Phone" or "Deselect phone" and if an user selects "Deselect phone", we do not see the user getting any calls as web RTC connection is unavailable.
If not, is there a way to remove this "Select Phone" or "Deselect phone" completely and use default connected phones only?
You might try GET /api/v2/telephony/providers/edges/phones/{phoneId} and see if any of the data on it is what you're looking for. I'm not aware of any general statistics for phones though. If you can't find the data you're looking for in the UI somewhere, it probably doesn't exist; there aren't many API endpoints that aren't implemented in the UI.
You might have better luck with your questions on the Genesys Cloud Community Forum since this is more about general use of the system than customization or questions about a particular endpoint.